Unsteady-State Energy Balances on Tanks: Interactive Simulations
These simulations were prepared using Mathematica. Download the free Wolfram player, and then download the simulation CDF file (link given below or click on figure to download). Try to predict the behavior when a parameter changes before using a slider to change that parameter. Screencasts below explain how to use these simulations.
In this simulation, one mole of an ideal gas expands when a valve is partly opened (by selecting the play button), from tank A (top) into tank B (bottom), which is initially at vacuum. Both tanks are well insulated. You can change the volume of tank B and the initial pressure of the gas with sliders. This also changes the initial temperature since the volume of tank A and the total number of moles do not change. When the pressure in the two vessels is equal, the valve closes.
Try to answer these questions before determining the answers with the simulation. Your retention will increase if you write down the reasons for your answers.
- When an ideal gas expands adiabatically from a tank at 200 kPa into a second empty identical tank until the pressures equalize, which tank has more gas (or do they each contain the same amount of gas)? Why?
- Is it possible for an ideal gas to expand adiabatically from a tank at 200 kPa into a second empty identical tank until half the gas has left the first tank? Why or why not?
In this Demonstration, a cylinder fitted with a weightless, frictionless piston initially contains a liquid slightly above its saturation pressure; the volume above the piston is initially under vacuum. You can select the initial mass and temperature of the liquid using the sliders. The final volume is fixed at 1.0 L. Expansion is enabled when the orange stop is removed. The piston then moves to the top of the cylinder as some liquid evaporates. The temperature drops due to evaporative cooling, while the final pressure reaches its saturation value. The liquid volume in the cylinder is exaggerated relative to the vapor volume for better visualization.
Try to answer these questions before determining the answers with the simulation. Your retention will increase if you write down the reasons for your answers.
- When liquid water expands into a vacuum in a closed, adiabatic cylinder, is the final temperature lower if the cylinder contains 1 g or 10 g? Why?
- Liquid water expands into a vacuum in a closed, adiabatic cylinder. The cylinder initially contains 10 g of liquid. If the initial temperature were increased, would the temperature change be larger or smaller? Why?
Compressed-gas dusters spray a gas such as difluoroethane (DFE) are used to remove dust from electronics. When gas exits the valve, liquid DFE in the container vaporizes to maintain vapor-liquid equilibrium. The energy to vaporize the liquid is obtained by cooling the remaining liquid; the container is modeled as adiabatic in this Demonstration. Select a plot (volume, moles, temperature, or pressure) using the buttons to display how that property changes with time. Animate the duster by clicking the play button next to “spray gas.” Spray continues until the temperature reaches -5°C (if stop at -5°C is selected); otherwise the spray stops at the time selected by the “time sprayed” slider when “adjust stopping time” is selected. The liquid and vapor DFE are assumed to be in equilibrium at all times.
Try to answer these questions before determining the answers with the simulation. Your retention will increase if you write down the reasons for your answers.
- The contents of a new compressed gas duster are initially 80% liquid by volume. After many uses, the contents are only 20% liquid by volume. When the duster is next used, does it get colder than when it was new? Why or why not?
- Does a compressed gas duster provide more “dusting” ability when it is new or used? Explain why.